摘要
讨论了一类具有阶段结构和庇护所效应的生态流行病模型,假设疾病仅在捕食种群之间传播,同时考虑了饱和发生率,首先利用Routh-Hurwitz判据研究了非负平衡点的局部稳定性,然后通过构造Lyapunov函数并结合LaSalle不变集原理得到了平衡点全局渐近稳定的充分条件,最后利用Pontryagin最大值原理研究了最优收获策略。
An eco-epidemiological model with stage structure and refuge effect is discussed,assuming that the disease only spread among predator populations,and saturated incidence rate is considered.First of all,the local stability of non-negative equilibria is studied by using Routh-Hurwitz criteria.Then,the sufficient conditions of the global asymptotical stability of the equilibria are obtained by constructing Lyapunov functions and combining with LaSalle’s invariance principle.Finally,the optimal harvesting strategy is investigated by using Pontryagin’s maximum principle.
作者
林风光
LIN Fengguang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《陕西理工大学学报（自然科学版）》
2023年第4期76-82,共7页
Journal of Shaanxi University of Technology:Natural Science Edition
基金
国家自然科学基金项目(11561041)。
关键词
阶段结构
稳定性
平衡点
收获
stage-structure
stability
equilibrium
harvesting
